By the way, I have been signed up for a pond game for quite some time Walter. I am just waiting for it to start.

The bet is a function of the number of players, the round, the average money per player, the standard deviation of the money, and your rank.

Plug all these into an equation, it spits out the bet you should make.

EdTrice: Ok, so throw us a bone. I assume your bet for the first round is a function of the number of players in the pond. Pick a number of players close (or even not close) to the 50 currently entered in the pond you are going to play in, say 47 (or 447). What would your first bet be?

Do you have a link to a copy of Nash's paper?

Let me not give away the system but still try and answer your question.

Is there a bet I can place on round 1 that will 100% guarantee that I do not fall into the pond? say $20,000 is the max, what is the most I can bet and still have me around for turn 2?

Answer: If there is NO COOPERATION among the other players, and the OBJECTIVE is to last for as long as possible, you can say with 100% certainty a bet of $19,999 will keep you around until the next turn.

Why is this so?

The only way to "lose" would be if everyone bet $20,000 (I am not sure if this would mean they all zero out anyway) which would imply massive cooperation, which would mean criterion #3 for unravelling the strategy has been evoked.

Granted, this is a ridiculous example, but you can go through a RETROGRADE ANALYSIS of survival through N rounds, then determine a bound you need never cross, then work your way back, then come up with a betting plan.

It is easier than you think, just play with it on paper (or in Excel) and you will see what I mean.

EdTrice: It is always possible, although statistically unlikely that every other player will bet their entire amount of the first round. In that case, you will fall in regardless of your wager. Thus there is no way you can 100% guarantee that you will win.

That is the definition of cooperation.

Given the rules of the game, players want to pursue the objective to keep money for as long as possible, not spend it all in one turn. When there is a majority going against the grain in such a fashion, the only factor of relevance is cooperation.

Read the paper, it is not my terminology

so lets say 20 players - 19 rounds. You want to keep at least 500 for round 19 to hopefully be enough to get bonus (19,500) - round 18 with 3 players left - safe to say someone will be below 1,000 left so a bet of 1,000 should be safe (down to 18,500)

etc... etc... Still a lot of guessing which will work for about 1/2 the game, but with so many players making unpredictable bets - it will be hard for a system to work.... in my opinion. (I would love to see the math though - would be interesting)

You have the right idea, but Excel can map out all of the bet ranges for you, and you can eliminate all scenarios where you lose, then just look at your survival numbers, then see the pattern.

... and congrats to drgnrdr who I'm sure will bet at least 999 on this next move in this game:

http://brainking.com/game/Pond?g=30

And look at the bets for that second to last round: 4500, 4501, and 4502, sending 4500 to the beach. And you guys tell me there is no system

EdTrice: There are obviously systems that guarantee a win for certain combinations of players/points/rounds, but there is no system that guarantees a win from an even start with 100% certainty (barring collusion) as you claim.

I disagree. You should also look up "The Hangman's Paradox" for a better explanation of why I made this claim. (hint: by making the claim I am influencing the play of others.)

That's all that will be said for now, see you all in the pond.

EdTrice: please answer my question which i asked before .. what kind of distribution do you assume for the bets of all players 1 one round to be ?
a gaussian distribution ? appearently not a straight distribution ? ;)

If you bet 19,999, in round 1, all it takes is ONE person to also bid 19,999, to mess you up. (No bonus is given for ties.)

interresting discussion.

but the question you should ask yourselves, as always when Ed posts something, should be what is the purpose of the post? what does the post accomplish? in what direction will it forcibly and predictably push the strategies of the participants? nice pretourney move, Ed

rabbitoid: *shrug* the reasons are his ... it does raise some curiousity in me though .. although it wont change my bets until i am 'converted' ;)

rabbitoid: With the group of players signed up, it will have little significant affect. Most participants don't read this board, they just play.

IF you win, youll be shouting " I am the greatest..bow down to me, my system works"

All I can see you doing WHEN you do lose, you will say " a few of you colaborated so as to make me lose" You will never admit that the loss was of your own fault or system failure

I hate to say this, but..ugh..I agree with Stevie.

If you bet 19,999, in round 1 , that would make you leve in the next few rounds because you would run out of points .... if you got all your points back +a bunus then that would work ...but for a bet of 19,999, you only get a 500 point bonus and lose the other 19,499

please dont start talking down on someone (for what reasons whatever) ... but investigate this theory .. dont be like the people at Dokkum hacking away at Bonifatius ;)

Most people here seem not to understand math. As with all games that need a mixed strategy, there can be no assured win, but there is a strategy that assures at least the same number of wins as the opponents. I don't know whether Ed has found this strategy, but nevertheless the strategy exists

Luke Skywalker: what edtrice says isnt a stratey which will let you win above average ... but

quote : the fullproof strategy as a function of the number of pond players per round that guarantees a win, provided nobody else has derived the same winning strategy?

ok, I hadn't read the previous posts carefully enough. That's not possible of course (except in some special situations, like you have more points than all others together). But then it depends very much on how he defines "cooperation", it could be different from the everyday meaning.

*nod*

My Jacuzzi pond starts in about 24 hours. I would like to ask everybody participating in this pond to play exactly in the way as if there were no EdTrice involved. That means NO cooperation. If we all want to see whether his (or the Nash's) system works, let us provide him with the required, i.e. fair conditions. Thanks.

reminds me of Gandhi's call to non violent non cooperation... Ed, I think that'll be the first time you'll have been compared to the british empire

If everyone starts from the same number, there can be no strategy that guarantees victory unless ridiculous assumptions are made. Of course using psychology and studying playing trends etc could give you an advantage and enable a player to win more than the expected number of games, the simple fact is that no strategy can guarantee victory.

Similar claims were made by hedgefund owners for a while as well, until Russia defaulted on debts amongst other things. It is simply impossible to model human behaviour with no uncertainty.

I think to make this a true "double blind" experiment, I should withdraw from the tournament, and ask if any player would like to make bets that I propose. When that person splashes into the pond, he or she can reveal themself, and you guys can make fun of the system at that time

EdTrice:
A big pond (like Pedro`s, you sign) is also a big advantage for a player,used math./stat. methods. You are clever.
But lets have a pond with 3 players/20000 points/no bonus.
A theoretical win is very "easy", you must only bet between the other two bets. But how ???

EdTrice: please .. release my curiousity sir .. what distribution do you assume ? my maths is ok .. my psychology is pretty bad ;)

EdTrice: I would like to see you stay in it to test your system - I mean no matter if you or anyone else is in it, you are always going to have the people who make strange bets which (in my opinion) will throw a wrench into any type of strategy or system - but would love to see if your system can overcome these normal odd bets.

trying to use a computer to win at pond is like using a prog to try and solve or beat poker. The best players have limited tells and a computer can't read them. Also, it just doesn't work because of a law, better than Nash's or anyone's theory: Murphy's Law. One of my extinction opponents recently pointed to inebriation as more powerful than any of that, though, which makes for a pretty unpredictable closed system.

If I stay in it, it will tempt cooperation, as I would be easy to identify as the one to try and undermine. If somehow we only showed who drops into the pond at the end of each round, it would probably work even better.

Maybe we need a "Dark Pond" variant

EdTrice: How would one go about intentionally eliminating another from a pond game?

EdTrice: And just why would everyone pick you to single out for defeat? Are you special? Or suffering from megalomania? I tend to think both from the way you've been carrying on here of late. Just play the game and be done with it. Though I might enjoy defeating you more than some of the other opponents, it is only because of how you act that makes this feeling in me. As I said earlier, "If you win, you win. If you lose, you lose, but I will rub it in."

As for a Dark Pond variant, that should be a funny game to play though it'd be all mystery. Especially if the running totals weren't shown either.

I keep seeing messages appear here, then there are none. I guess somebody I have on HIDE is posting.

Thad: Easy Thad. There are say 10 people remaining. You message 8 of your choice and say "bet this" which is an otherwise ridiculously high bid. All who remain suffer, but suffer cooperatively, which sends the 1 you did not message into the pond.

EdTrice: I see it as you are trying to sidle out of your previous claims...if you remove yourself..then you are a loser to start with Ed, if you stay and lose..you will be less of a loser..if you win..we will be amazed and hail you as a new world leader

EdTrice: If that happens (which is unlikely because you'd have to get ALL of the remaining players to do it), then it would be clear by the unusually high bets that it had been done, so I don't see you being 'marked' as a problem.

Stevie: My previous claims were made with the caveat, so why don't you go back and read them?

On second thought, you guys have taken all the fun out of it.

so you turn chicken and have left it I see

<sarcasm> no-one expected that did they </sarcasm>

Ed has withdrawn from the run he was entered in. I'm convinced his system was legit. ;-)

Trice - Please sign back up for that pond - I would like to see your system in play to see if it really work.

To have someone else do it for you, then tell us after the fact who is was will not work since we are unable to look back at previous round bets and would need to know this information before hand.

But if you are going to stay out, why not share this excel spreedsheet - wolf@coan.net

Apparently i forgot to add the tags

<joke>

Assume the highest bet (other than yours) = H. The lowest bet = L.

Your bet (B) is determined by:
if (H>L+500) { B=L+1 } else { B=H+1 }

There is the mathematically certain way of winning!

</joke>